Question

A natural number when divided by 18 leaves remainder of 14 and when divided by 24 leaves a remainder of 20. Find the least possible value it can take.

Answer 1

Hi,

➡️Answer: 68

➡️Solution:

A natural number when divided by 18 leaves remainder of 14 and when divided by 24 leaves a remainder of 20.

As 18-14 = 4

24-20 = 4

Since difference is same.

So,we take LCM of 18 and 24, and then subtract 4

Prime factors of
$18 = 2 \times 3 \times 3$

prime factors of
$24 = 2 \times 2 \times 2 \times 3$
LCM (18,24) =
$2 \times 2 \times 2 \times 3 \times 3 \\ \\ = 72$
Subtract 4 from 72: 72-4

= 68

So ,68 is that least number when when divided by 18 leaves remainder of 14 and when divided by 24 leaves a remainder of 20.

Hope it helps you.

Answer 2

Let the natural number be "x".

x%18 = 14   [% -> modulo division sign used for indicating the remainder]

and x%24 = 20.

It means  

x=18*n+14

Where n = 0,1,2…  

If we divide x by 24 then it gives the remainder 20

x=24*m+20

For m=2 and n=3 we get, the same value of "x".

i.e. x = 68. [Ans]

Therefore the least possible value we can take in order to get the above result and satisfy the condition as well is 68.